Precalculus Examples

$- \frac{1}{3} x + [\begin{array}{c} 15 & 21 \\ 0 & 1 \end{array}] = [\begin{array}{c} 3 & 27 \\ 4 & 6 \end{array}]$

Step 1

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} + [\begin{array}{c} 15 & 21 \\ 0 & 1 \end{array}] = [\begin{array}{c} 3 & 27 \\ 4 & 6 \end{array}]$

Step 2

Move all terms not containing a variable to the right side.

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Step 2.1

Subtract $[\begin{array}{c} 15 & 21 \\ 0 & 1 \end{array}]$ from both sides of the equation.

$- \frac{x}{3} = [\begin{array}{c} 3 & 27 \\ 4 & 6 \end{array}] - [\begin{array}{c} 15 & 21 \\ 0 & 1 \end{array}]$

Step 3

Simplify the right side.

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Step 3.1

Subtract the corresponding elements.

$- \frac{x}{3} = [\begin{array}{c} 3 - 15 & 27 - 21 \\ 4 - 0 & 6 - 1 \end{array}]$

Step 3.2

Simplify each element.

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Step 3.2.1

Subtract $15$ from $3$ .

$- \frac{x}{3} = [\begin{array}{c} - 12 & 27 - 21 \\ 4 - 0 & 6 - 1 \end{array}]$

Step 3.2.2

Subtract $21$ from $27$ .

$- \frac{x}{3} = [\begin{array}{c} - 12 & 6 \\ 4 - 0 & 6 - 1 \end{array}]$

Step 3.2.3

Subtract $0$ from $4$ .

$- \frac{x}{3} = [\begin{array}{c} - 12 & 6 \\ 4 & 6 - 1 \end{array}]$

Step 3.2.4

Subtract $1$ from $6$ .

$- \frac{x}{3} = [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 4

Multiply both sides by $- 3$ .

$- 3 (- \frac{x}{3}) = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $3$ .

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Step 5.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5.1.4

Rewrite the expression.

$- - x = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5.2

Multiply $- 1$ by $- 1$ .

$1 x = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5.3

Multiply $x$ by $1$ .

$x = - 3 [\begin{array}{c} - 12 & 6 \\ 4 & 5 \end{array}]$

Step 5.4

Multiply $- 3$ by each element of the matrix.

$x = [\begin{array}{c} - 3 \cdot - 12 & - 3 \cdot 6 \\ - 3 \cdot 4 & - 3 \cdot 5 \end{array}]$

Step 5.5

Simplify each element in the matrix.

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Step 5.5.1

Multiply $- 3$ by $- 12$ .

$x = [\begin{array}{c} 36 & - 3 \cdot 6 \\ - 3 \cdot 4 & - 3 \cdot 5 \end{array}]$

Step 5.5.2

Multiply $- 3$ by $6$ .

$x = [\begin{array}{c} 36 & - 18 \\ - 3 \cdot 4 & - 3 \cdot 5 \end{array}]$

Step 5.5.3

Multiply $- 3$ by $4$ .

$x = [\begin{array}{c} 36 & - 18 \\ - 12 & - 3 \cdot 5 \end{array}]$

Step 5.5.4

Multiply $- 3$ by $5$ .

$x = [\begin{array}{c} 36 & - 18 \\ - 12 & - 15 \end{array}]$